Agent-based load balancing on homogeneous minigrids: macroscopic modeling and characterization

In this paper, we present a macroscopic-characterization of agent-based load balancing in homogeneous minigrid environments. The agent-based load balancing is regarded as agent distribution from a macroscopic point of view. We study two quantities on minigrids: the number and size of teams where agents (tasks) queue. In macroscopic modeling, the load balancing mechanism is characterized using differential equations. We show that the load balancing we concern always converges to a steady state. Furthermore, we show that load balancing with different initial distributions converges to the same steady state gradually. Also, we prove that the steady state becomes an even distribution if and only if agents have complete knowledge about agent teams on minigrids. Utility gains and efficiency are introduced to measure the quality of load balancing. Through numerical simulations, we discuss the utility gains and efficiency of load balancing in different cases and give a series of analysis. In order to maximize the utility gain and the efficiency, we theoretically study the optimization of agents' strategies. Finally, in order to validate our proposed agent- based load balancing mechanism, we develop a computing platform, called simulation system for grid task distribution (SSGTD). Through experimentation, we note that our experimental results in general confirm our theoretical proofs and numerical simulation results from the proposed equation system. In addition, we find a very interesting phenomenon, that is, agent-based load balancing mechanism is topology-independent.